Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II: Applications

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Atsushi Yagi

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II

Applications

Atsushi Yagi

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English

Springer Verlag, Singapore
13 August 2021

Functional analysis & transforms; Integral calculus & equations

Series: SpringerBriefs in Mathematics

Summary
Details

This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensionalspaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.

By: Atsushi Yagi
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 1st ed. 2021
Dimensions: Height: 235mm, Width: 155mm,
Weight: 226g
ISBN: 9789811626623
ISBN 10: 9811626626
Series: SpringerBriefs in Mathematics
Pages: 128
Publication Date: 13 August 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active